The field of signal processing is concerned with the analysis, interpretation and manipulation of signals. Many technologies employ various techniques of signal processing on sound, images, biological signals such as EKG, radar signals, and many other types of signals in order to store and reconstruct signals, separate valid information from noise (e.g., water, air, land craft identification by radar or sonar), compress (e.g., video or audio compression), and perform feature extraction (e.g., speech-to-text conversion). The current methods of signal processing technology may be sufficient for some signals. However, they are incapable of accurately analyzing signals that contain data sets where (1) the total data set is too short, (2) the data is non-stationary, and (3) the data represents a nonlinear process.
In signal processing technology, it is necessary to decompose composite waveforms representing the transmission of data. The traditional methods for transmitting data rely on a two-dimensional display usually in the form of a sine wave, modified to contain data. Data may be stored by modulating the amplitude, frequency, phase or a combination of the foregoing.
Referring to FIG. 1A, a traditional view of a waveform 10 is shown, having variations in amplitude over time. It is formed by combining waves of multiple frequencies 12 and 14, as shown in FIGS. 1B and 1C. Such two-dimensional representations do not fully represent what is happening with a three-dimensional waveform, and are not adequate for completely analyzing a composite waveform 20, as shown in FIG. 2.
Historically, researchers have used Fourier transforms to analyze signals. As a result, the term “spectrum” has become almost synonymous with the Fourier transform of the data. A Fourier analysis transforms the time data into the frequency domain, selects windows of data and resolves the fundamental waveforms that compose the wave. However, Fourier originally intended for his transform to be used on signals that are harmonically related if data does not continue infinitely. Current adaptations of Fourier's transform are not able to necessarily make these same assumptions. As a result, data extracted using this method may not be accurately represented.
Most real world composite waveforms involve signals that are not periodic, predictable, linear, or harmonically related. For example, speech is constantly changing in frequency, amplitude and tone and thus requires precise formant tracking over time of streaming signal data. Accordingly, the audio signal must instantly be broken down into its varying formant frequencies and tracked over time to accurately determine what is being said. Spectral analysis may provide an idea of what the formants are in a particular sound clip in a window sample, but it cannot describe exactly what frequencies were doing at each point in time, that is from sample to sample.
In an attempt to minimize the limitations of the Fourier Transform, new methods have been developed. These methods include, but are not limited to, Fast Fourier Transform (FFT, IFT), Short-Time Fourier Transform (STFT), Wavelet Analysis (including Chirplet Transform), Empirical Orthogonal Function Expansion (EOF, PCA, SVD), and others. Although these methods have improved the process of spectral signal analysis, they still fall short of the needed flexibility and resolution for specific signal analysis applications.
Recently, a type of spectral analysis has begun to evolve, sometimes referred to as Instantaneous Frequency Analysis or IFA. The premise behind Instantaneous Frequency Analysis is to analyze waveforms converted to digital form at each sample point in time, rather than using a time window as is done in the Fourier Transform. It is expected that this approach will provide a more accurate representation of the makeup of composite signals than the traditional spectral analysis would allow, even under the harshest conditions where data is non-linear, non-stationary, and too short to properly analyze using traditional methods. In the IFA approach, the Fourier Transform is used very little if any.
One example of IFA technology is shown in U.S. Pat. No. 6,862,558 (Huang), in which an acoustical signal is decomposed into a set of “intrinsic mode functions” (IMFs), that are then transformed into the Hilbert spectrum for analysis. The Huang process uses approximation methods to develop IMFs, based on determining the mean of maximum and minimum points of a composite waveform. This approximation approach may not be sufficiently precise for many applications. Moreover, the Huang process does not appear to be able to sense phase shifting of signals, detect peaks in signal components, or distinguish between frequencies less than 2.5 to 1 in frequency relation because these composite waves appear as a single amplitude modulated waveform.
Accordingly, there is a need for methods to instantaneously and precisely analyze composite waveforms, such as real time acoustical signals, for use in a great variety of applications.